What is Lisp-Stat?

A statistical analysis environment written in Common Lisp

Lisp-Stat is a domain specific language (DSL) for statistical analysis and machine learning. It is targeted at statistics practioners with little or no experience in programming.

Lisp has a history of being deployed for domain experts to use, and it’s a great language for beginners; the Symbolics Graphics Division wrote the software used by graphic artists to develop scenes in several films prior the rise of Pixar. One of the first statistical systems developed, XLisp-Stat, was a contemporary to R until the primary author joined the ‘R Core’ group.

Raisons d’être

There are several reasons to prefer Lisp-Stat over R or Python. The first is that it is fast. Lisp compilers produce native executable code that is nearly as fast as C. The Common Lisp numerical tower has support for rational numbers, which is a natural way to work with samples. For example an experiment may produce 11598 positives out of a sample of 25000. With exact rational arithmatic, there is no need to force everything to a float, the value is just what the experiment said: 11598 / 25000.

Probably the most important reason though is given in the paper by Ross Ihaka, one of the originators of the R language, Lisp as a Base for a Statistical Computing System about the deficiencies in R and the inability to compile to machine code (among other issues). The same is true of Python. In that paper he argues for Lisp as a replacement for R.

Not only does Common Lisp provide a compiler that produces machine code, it has native threading, a rich ecosystem of code libraries, and a history of industrial deployments, including:

  • Credit card authorisation at Amex (Authorizers Assistant)
  • US DoD logistics (and more that we do not know of)
  • CIA and NSA are big users based on Lisp sales
  • DWave, HSL and Rigetti use lisp for programming their quantum computers
  • Apple’s Siri was originally written in Lisp
  • Amazon got started with Lisp & C; so did Y-combinator
  • Google’s flight search engine is written in Common Lisp
  • AT&T used a stripped down version of Symbolics Lisp to process CDRs in the first IP telephony switches

If Lisp is good enough for those applications, it very likely can meet the needs of an enterprise deployment today.

Relationship to XLISP-Stat

Although inspired by Tierney’s XLisp-Stat, this is a reboot in Common Lisp. XLisp-Stat code is unlikely to run except in trivial cases, and existing XLisp-Stat libraries can be ported with the assistance of the XLS-Compat system.

In developing the system, I wanted to avoid the lisp curse, so selected the best existing libraries where possible, developed what didn’t exist, and documented them all in an attempt to make the learning curve a gentle slope.

Library Consolidation

Eventually, we hope for a consolidation of lisp statistical libraries in order to achieve a critical mass in the domain. The reasons for moving in this direction were described in an article some years ago entitled Consolidating Common Lisp Libraries. Whilst historical precedent is against us, that does not mean we won’t try.

Core Systems

Lisp-Stat is composed of several systems (projects), each independently useful and brought together under the Lisp-Stat umbrella. Dependencies between systems have been minimised to the extent possible so you can use them individually without importing all of Lisp-Stat.


A data frame is a data structure conceptually similar to a R data frame. It provides column-centric storage for data sets where each named column contains the values for one variable, and each row contains one set of observations. For data frames, we use the ‘tibble’ from the tidyverse as inspiration for functionality.

Data frames can contain values of any type. If desired, additional attributes, such as the numerical type, unit and other information may be attached to the variable for convenience or efficiency. For example you could specify a unit of length, say m/s (meters per second), to ensure that mathmatical operations on that variable always produce lengths (though the unit may change).


The Data Frame I/O system provides input and output operations for data frames. A data frame may be written to and read from files, strings or streams, including network streams or relational databases.


Select is a facility for selecting portions of sequences or arrays. It provides:

  • An API for making selections (elements selected by the Cartesian product of vectors of subscripts for each axis) of array-like objects. The most important function is select. Unless you want to define additional methods for select, this is pretty much all you need from this library.
  • An extensible DSL for selecting a subset of valid subscripts. This is useful if, for example, you want to resolve column names in a data frame in your implementation of select, or implementing filtering based on row values.

Array Operations

This library is a collection of functions and macros for manipulating Common Lisp arrays and performing numerical calculations with them. The library provides shorthand codes for frequently used operations, displaced array functions, indexing, transformations, generation, permutation and reduction of columns. Array operations may also be applied to data frames, and data frames may be converted to/from arrays.

Special Functions

This library implements numerical special functions in Common Lisp with a focus on high accuracy double-float calculations. These functions are the basis for the statistical distributions functions, e.g. gamma, beta, etc.


Cephes.cl is a CFFI wrapper over the Cephes Math Library, a high quality C implementation of statistical functions. We use this both for an accuracy check (Boost uses these to check its accuracy too), and to fill in the gaps where we don’t yet have common lisp implementations of these functions.

Numerical Utilities

Numerical Utilities is the base system that most others depend on. It is a collection of packages providing:

  • num=, et. al. comparison operators for floats
  • simple arithmetic functions, like sum and l2norm
  • element-wise operations for arrays and vectors
  • intervals
  • special matrices and shorthand for their input
  • sample statistics
  • Chebyshev polynomials
  • quadratures
  • univariate root finding
  • horner’s, simpson’s and other functions for numerical analysis


This is the top level system that uses the other packages to create a statistical computing environment. It is also the location for the ‘unified’ interface, where the holes are plugged with third party packages. For example cl-mathstats contains functionality not yet in Lisp-Stat, however its architecture does not lend itself well to incorporation via an ASDF depends-on, so as we consolidate the libraries, missing functionality will be placed in the Lisp-Stat system. Eventually parts of numerical-utilities, especially the statistics functions, will be relocated here.



Emacs, with the slime package is the most tested IDE and the one the authors use. If you are using one of the starter lisp packages mentioned in the getting started section, this will have been installed for you. Otherwise, slime/swank is available in quicklisp and clpm.

Jupyter Lab

Jupyter Lab and common-lisp-jupyter provide an environment similar to RStudio for working with data and performing analysis. The Lisp-Stat analytics examples use Jupyter Lab to illustrate worked examples based on the book, Introduction to the Practice of Statistics.

Clozure Common Lisp

On MacOS, Clozure Common Lisp, provides a graphical editing environment with a built-in editor and menu driven system for working with Lisp-Stat.


Generally, we are prioritising these systems for development:

  1. Data Frame
  2. Plotting
  3. Special Functions & Distributions

In terms of priority, 1 & 2 are equally rated, and special-functions/distributions lower priority because we have a Cephes available now. As well, the knowledge of numerical methods required for accurate implementation is somewhat more limited.

For the most part, implementation priority is determined by the features required when working through the Lisp-Stat examples and the basic tutorial. Being able to execute all the examples in these two documents is the first MVP milestone. If you see something in one of these documents that does not work yet it will be a good starter issue for a contribution (you’ll have to look at the source for the document, as functionality that isn’t implemented will have been commented out).


Tamas Papp was the original author of many of these libraries. Starting with relatively clean, working, code that solves real-world problems was a great start to the development of Lisp-Stat.

What next?

Get Started
R Users

Last modified 07 October 2021: Update for Lisp-Stat 2.0 (c5b846d)